Dual Properties of the Relative Belief of Singletons

2010

Ann Math Artif Intell

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The study of the interplay between belief and probability can be posed in a geometric framework, in which belief and plausibility functions are represented as points of simplices in a Cartesian space. Probability approximations of belief functions form two homogeneous groups, which we call "affine" and "epistemic" families. In this paper we focus on relative plausibility, belief, and uncertainty of probabilities of singletons, the "epistemic" family. They form a coherent collection of probability transformations in terms of their behavior with respect to Dempster's rule of combination. We investigate here their geometry in both the space of all pseudo belief functions and the probability simplex, and compare it with that of the affine family. We provide sufficient conditions under which probabilities of both families coincide.Keywords Theory of evidence · Probability transformation · Geometric approach · Relative plausibility and belief of singletons · Relative uncertainty on the probabilities of singletons Mathematics Subject Classifications (2010) 62A99 · 62C86 · 60A99 · 60D99

“…On the other side, both pl b [31] and b [10] commute with respect to Dempster's rule of combination of belief or plausibility functions, respectively. Let us see why in greater detail.…”

Section: A Geometric Interplay Of Belief and Probabilitymentioning

confidence: 96%

Section: Contributionsmentioning

confidence: 98%

Section: A Geometric Interplay Of Belief and Probabilitymentioning

confidence: 99%

“…The last two transformations meet a set of dual properties [6] with respect to ⊕. We call them the epistemic family.…”

mentioning

confidence: 99%

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Geometry of relative plausibility and relative belief of singletons

2010

Ann Math Artif Intell

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“…Some preliminary analyses of the relative belief transform and its close relationship with the (relative) plausibility transform have been presented in [9,10]. A detailed discussion of the geometrical properties ofb andpl has been given in [11].…”

Section: Introductionmentioning

confidence: 99%

Game-Theoretical Semantics of Epistemic Probability Transformations

Advances in Intelligent and Soft Computing

2012

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Probability transformation of belief functions can be classified into different families, according to the operator they commute with. In particular, as they commute with Dempster's rule, relative plausibility and belief transforms form one such "epistemic" family, and possess natural rationales within Shafer's formulation of the theory of evidence, while they are not consistent with the credal or probability-bound semantic of belief functions. We prove here, however, that these transforms can be given in this latter case an interesting rationale in terms of optimal strategies in a non-cooperative game.

Semantics of the Relative Belief of Singletons

Advances in Soft Computing

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